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ability power ratio

i don't understand what ability power ratio of a spell means exactly and how does it work. Can someone explain this please? It doesn't have to be a perfect explanation... any comment that may shed some light on this topic will be greatly appreciated.

It's what amount of your Ability Power your abilities gain in extra damage. Say you have 100 Ability Power, and have one ability with a 1:1 ratio and one with a 0.5:1 ratio. The first would deal 100 extra damage (or healing, if it was a healing ability), while the second would gain 50 (100 * 0.5) extra damage or healing.

in simple terms, the higher the ratio, the more the spell benefits from ability power.
If you are playing a caster with high ratios, then by all means go for more ability power
If he has low ratios, then just go for magic armor penetration instead.

To figure out the damage you're going to do, you need to take the damage the spells does, add the AP multiplied by the AP ratio, total up your spell pen, then figure the math for how much their spell resistance is, and then how much of your damage will be finally reduced after everything is is figured in.

Or just, you know, get a ton of AP and just drop nukes on people. Don't worry about the actual numbers and enjoy

You can look the champion up. Most abilities will say something like "deals 50/75/100/125/150 (+.75) dmg". The first set of numbers are the base dmg for each level of the ability, the number in paranthesis is the AP ratio. So, in the above, if I had 100 AP and was using the ability at level 3, I would do 100+(100*0.75) = 175 dmg (note that this number would then be modified by magic penetration, magic resist, etc.). guides in the guide section will also list champions AP ratios (well, the good ones will).

Alternatively, while in the game, you can see the actual numbers. When looking at the description of the above ability, you would be told that it would do "100 (+75)" dmg. The number in the paranthesis is the bonus from AP, allowing you to back calculate it (or at least estimate it if you don't have nice round numbers).

As a final note, abilities that do damage / second (like fiddle's crowstorm or rammus's tremors) list their dmg and AP for each second. Thus, Rammus's tremors might list dmg as 100 (+0.3), that damage is applied for each second. Thus, if you could keep someone in range of your tremmors for the entire 8 second duration, you would actually do 800 (+2.4) dmg. Using the previous 100 AP, that would translate into an extra 240 dmg over 8 seconds (and not the 30 dmg that it would first seem to be).